The procedure of computing robustness bounds is a layer-by-layer process computing from the first hidden layer to the last output layer. To compute global robustness bounds, we need to compute the linear bounds of every layer in CNNs. For details of the whole computing procedure, readers can refer to the work [1]}.
[Upper/Lower linear bounds]
Let \(f^k_i(x)\)  be the function of the \(i^{th}\)  Neuron in the \(k^{th}\)  layer of neural network \(F\) , with \(x\in [l,u]\subset \mathbb {R}^{n},a_u,a_l,b_u,b_l\in \mathbb {R}^{n}\)  and
\(u_i(x)=a_ux+b_u,l_i(x)=a_lx+b_l\) 
